>I see no reason to suppose that this visualization would change. Whatever we take as the unit of area or the unit of volume, we would, sooner or later, need to show that the area of a rectangle is proportional to the product of its two dimensions, while the volume of a right parallelopipedis proportional to the product of its three.

I was thinking along those lines. Of course you could keep your chosen unit and shape, but you'd be pushed into considering at least parallelograms and parallelepipedsas the shapes that support visualizing the growth in a way that makes the derivatives plain. I didn't consider one would be forced to entertain right angles necessarily.